TGF: A New MATLAB-based Software for Terrain-related Gravity Field Calculations

2020 ◽  
Author(s):  
Meng Yang ◽  
Christian Hirt ◽  
Roland Pail
Keyword(s):  
Gravity Field ◽  
Adaptive Algorithm ◽  
Computation Time ◽  
Spherical Approximation ◽  
Constant Density ◽  
The Earth ◽  
Digital Elevation ◽  
Gravity Effects ◽  
Residual Terrain Modelling

<p>With knowledge of geometry and density-distribution of topography, the residual terrain modelling (RTM) technique has been broadly applied in geodesy and geophysics for the determination of the high-frequency gravity field signals. Depending on the size of investigation areas, challenges in computational efficiency are encountered when using an ultra-high-resolution digital elevation models (DEM) in the evaluation of Newtonian integration. This paper presents a new MATLAB-based program, terrain gravity field (TGF), for the accurate and efficient determination of the terrain-related gravity field based on an adaptive algorithm. Depending on the attenuation character of gravity field with distance, the adaptive algorithm divides the integration masses into four zones, and adaptively combines four types of geometries and DEMs with different spatial resolutions. The most accurate but least efficient polyhedron together with the finest DEM are only considered for the innermost zone, while prism approximation for the second zone, the third zone with the more efficient tesseroid and a coarse DEM, and the most efficient but least accurate point-mass with the coarsest DEM for distant masses. Compared to some publicly available algorithms depending on one type of geometric approximation, the TGF achieves accurate modelling of gravity field and greatly reduces the computation time. Besides, the TGF software allows to calculate ten independent elements of gravity field, supports two types of density inputs (constant density value and digital density map), and considers the sphericity of the Earth by involving spherical approximation and ellipsoidal approximation. Further to this, the TGF software is also capable of delivering the gravity field of full-scale topographic gravity field implied by masses between the Earth’s surface and mean sea level. Results from internal and external numerical validation experiments of TGF confirmed its accuracy of sub-mGal level. Based on TGF, the trade-off between accuracy and efficiency, values for the spatial resolution and extension of topography models are recommended. The TGF software has been extensively tested and recently been applied in the SRTM2gravity project to convert the global 3” SRTM topography to implied gravity effects at 28 billion computation points. This confirms TGF the capability of dealing with large datasets.</p>

scholarly journals TGF: A New MATLAB-based Software for Terrain-related Gravity Field Calculations

2020 ◽  
Vol 12 (7) ◽  
pp. 1063
Author(s):  
Meng Yang ◽  
Christian Hirt ◽  
Roland Pail
Keyword(s):  
Density Distribution ◽  
Gravity Field ◽  
Mass Density ◽  
Computation Time ◽  
Spherical Approximation ◽  
Constant Density ◽  
Forward Modelling ◽  
Gravity Effects ◽  
Residual Terrain Modelling ◽  
Elevation Model

With knowledge of geometry and density-distribution of topography, the residual terrain modelling (RTM) technique has been broadly applied in geodesy and geophysics for the determination of the high-frequency gravity field signals. Depending on the size of investigation areas, challenges in computational efficiency are encountered when using an ultra-high-resolution digital elevation model (DEM) in the Newtonian integration. For efficient and accurate gravity forward modelling in the spatial domain, we developed a new MATLAB-based program called, terrain gravity field (TGF). Our new software is capable of calculating the gravity field generated by an arbitrary topographic mass-density distribution. Depending on the attenuation character of gravity field with distance, the adaptive algorithm divides the integration masses into four zones, and adaptively combines four types of geometries (i.e., polyhedron, prism, tesseroid and point-mass) and DEMs with different spatial resolutions. Compared to some publicly available algorithms depending on one type of geometric approximation, this enables accurate modelling of gravity field and greatly reduces the computation time. Besides, the TGF software allows to calculate ten independent gravity field functionals, supports two types of density inputs (constant density value and digital density map), and considers the curvature of the Earth by involving spherical approximation and ellipsoidal approximation. Further to this, the TGF software is also capable of delivering the gravity field of full-scale topographic gravity field implied by masses between the Earth’s surface and mean sea level. In this contribution, the TGF software is introduced to the geoscience community and its capabilities are explained. Results from internal and external numerical validation experiments of TGF confirmed its accuracy at the sub-mGal level. Based on TGF, the trade-off between accuracy and efficiency, values for the spatial resolution and extension of topography models are recommended. The TGF software has been extensively tested and recently been applied in the SRTM2gravity project to convert the global 3” SRTM topography to implied gravity effects at 28 billion computation points. This confirms the capability of TGF for dealing with large datasets. Together with this paper, the TGF software will be released in the public domain for free use in geodetic and geophysical forward modelling computations.

scholarly journals A computationally efficient depression-filling algorithm for digital elevation models applied to proglacial lake drainage

2016 ◽  
Author(s):  
Constantijn J. Berends ◽  
Roderik S. W. van de Wal
Keyword(s):  
Geographical Area ◽  
Computation Time ◽  
Equation Model ◽  
Limiting Factor ◽  
Computationally Efficient ◽  
Digital Elevation ◽  
Lake Drainage ◽  
Elevation Model ◽  
Flood Fill

Abstract. We present and evaluate several optimizations to a standard flood-fill algorithm in terms of computational efficiency. As an example, we determine the land/ocean-mask for a 1 km resolution digital elevation model (DEM) of North America and Greenland, a geographical area of roughly 7000 by 5000 km (roughly 35 million elements), about half of which is covered by ocean. Determining the land/ocean-mask with our improved flood-fill algorithm reduces computation time by 90 % relative to using a standard stack-based flood-fill algorithm. In another experiment, we use the bedrock elevation, ice thickness and geoid perturbation fields from the output of a coupled ice-sheet–sea-level equation model at 30,000 years before present and determine the extent of Lake Agassiz, using both the standard and improved versions of the flood-fill algorithm. We show that several optimizations to the flood-fill algorithm used for filling a depression up to a water level, that is not defined at forehand, decrease the computation time by up to 99 %. The resulting reduction in computation time allows determination of the extent and volume of depressions in a DEM over large geographical grids or repeatedly over long periods of time, where computation time might otherwise be a limiting factor.

Bouguer Redeemed: The Successful 1737-1740 Gravity Experiments on Pichincha and Chimborazo

2010 ◽  
Vol 29 (1) ◽  
pp. 1-25 ◽  
Author(s):  
John Smallwood
Keyword(s):  
Plumb Line ◽  
Near Surface ◽  
The Earth ◽  
Digital Elevation ◽  
The Mean ◽  
Good Determination ◽  
Elevation Model ◽  
Academy Of Sciences ◽  
Regional Gravity

During the 1735-1745 French Academy of Sciences expedition to Peru, Pierre Bouguer conducted two experiments confirming Newtonian gravitational attraction and estimating the mean density of the Earth. One set of experiments determined the variation in gravity with altitude using a pendulum at sea level, Quito (2,860 m) and the summit of Pichincha (4,784 m). Qualitatively correct, Bouguer reported a smaller decrease in gravity than that predicted from altitude increase alone, but he calculated that the mean density of the Earth was nearly five times that of the near-surface rocks, an overestimate by a factor of at least two. The better reported experiment was an attempt to detect the deflection of the vertical near the mountain Chimborazo. There was a large difference between Bouguer's predicted plumb-line deflection, 103", and that which he and La Condamine measured, just 7". I have investigated both experiments using a digital elevation model to compute the vertical and horizontal components of the gravity field caused by topography, and include the regional gravity signature of the Andean crustal root. The modelling indicates not only that Bouguer's pendulum measurements were extremely accurate, but also that his observations allow a good determination of the significant isostatic effect. In contrast, on Chimborazo, contrary to recent suggestions, isostatic effects are negligible, and Bouguer's deflection was, within error, in line with the modelled plumb-line deflection from topography. Both Bouguer's pendulum and plumb-line measurements were reliable and therefore he should now be redeemed from any inference of failure.

scholarly journals Neutrino Propagation in Matter

2013 ◽  
Vol 2013 ◽  
pp. 1-33 ◽  
Author(s):  
Mattias Blennow ◽  
Alexei Yu. Smirnov
Keyword(s):  
Neutrino Mass ◽  
Thin Layers ◽  
Constant Density ◽  
Mass Hierarchy ◽  
Neutrino Mass Hierarchy ◽  
The Earth ◽  
Density Perturbations ◽  
Small Density ◽  
Neutrino Propagation

We describe the effects of neutrino propagation in the matter of the Earth relevant to experiments with atmospheric and accelerator neutrinos and aimed at the determination of the neutrino mass hierarchy and CP violation. These include (i) the resonance enhancement of neutrino oscillations in matter with constant or nearly constant density, (ii) adiabatic conversion in matter with slowly changing density, (iii) parametric enhancement of oscillations in a multilayer medium, and (iv) oscillations in thin layers of matter. We present the results of semianalytic descriptions of flavor transitions for the cases of small density perturbations, in the limit of large densities and for small density widths. Neutrino oscillograms of the Earth and their structure after determination of the 1–3 mixing are described. A possibility to identify the neutrino mass hierarchy with the atmospheric neutrinos and multimegaton scale detectors having low energy thresholds is explored. The potential of future accelerator experiments to establish the hierarchy is outlined.

scholarly journals Effect of the Gravitational Aberration on the Earth Gravity Field

2021 ◽  
Vol 56 (1) ◽  
pp. 1-9
Author(s):  
Janusz B. Zieliński ◽  
Vladimir V. Pashkevich
Keyword(s):  
Gravity Field ◽  
Orbit Determination ◽  
Artificial Satellites ◽  
Finite Speed ◽  
Earth Gravity Field ◽  
Earth Gravity ◽  
The Earth ◽  
First Approximation ◽  
Classic Theory

Abstract Discussing the problem of the external gravitational potential of the rotating Earth, we have to consider the fundamental postulate of the finite speed of the propagation of gravitation. This can be done using the expressions for the gravitational aberration compared to the Liénard–Wiechert solution of the retarded potentials. The term gravitational counter-aberration or co-aberration is introduced to describe the pattern of the propagation of the gravitational signal emitted by the rotating Earth. It is proved that in the first approximation, the classic theory of the aberration of light can be applied to calculate this effect. Some effects of the gravitational aberration on the external gravity field of the rotating Earth may influence the orbit determination of the Earth artificial satellites.

scholarly journals An Analysis of Choosing Gravity Anomalies for Solving Problems in Geodesy, Geophysics and Environmental Engineering

2020 ◽  
Author(s):  
Vytautas Puškorius ◽  
Eimuntas Paršeliūnas ◽  
Petras Petroškevičius ◽  
Romuald Obuchovski
Keyword(s):  
Gravity Field ◽  
Gravity Anomalies ◽  
Environmental Engineering ◽  
Correct Selection ◽  
Earth’S Gravity Field ◽  
The Earth ◽  
Pure Gravity ◽  
Geodynamic Processes ◽  
Selection Of

Gravity anomalies provide valuable information about the Earth‘s gravity field. They are used for solving various geophysical and geodetic tasks, mineral and oil exploration, geoid and quasi-geoid determination, geodynamic processes of Earth, determination of the orbits of various objects, moving in space around the Earth etc. The increasing accuracy of solving the above mentioned problems poses new requirements for the accuracy of the gravity anomalies. Increasing the accuracy of gravity anomalies can be achieved by gaining the accuracy of the gravimetric and geodetic measurements, and by improving the methodology of the anomalies detection. The modern gravimetric devices allow to measure the gravity with an accuracy of several microgals. Space geodetic systems allow to define the geodetic coordinates and ellipsoidal heights of gravimetric points within a centimeter accuracy. This opens up the new opportunities to calculate in practice both hybrid and pure gravity anomalies and to improve their accuracy. In this context, it is important to analyse the possibilities of detecting various gravity anomalies and to improve the methodology for detecting gravity anomalies. Also it is important the correct selection of the gravity anomalies for different geodetic, geophysical and environmental engineering tasks. The modern gravity field data of the territory of Lithuania are used for the research.

scholarly journals Proposals for an Improved Nutation Formula

1990 ◽  
Vol 141 ◽  
pp. 148-148
Author(s):  
E. Groten ◽  
S. Y. Zhu
Keyword(s):  
Gravity Field ◽  
Ocean Tide ◽  
Combined Model ◽  
Earth Gravity ◽  
The Earth ◽  
Low Degree ◽  
Vlbi Data ◽  
Nutation Series ◽  
New Formula

There are a variety of reasons why in geodesy an improved formula for nutation is needed; related topics of interest are the determination of time-dependences in low degree zonals of the earth gravity field, ocean tide modeling, determination of odd harmonics of gravity field etc. in satellite geodesy. A combined model of deterministic and stochastic components is used in order to evaluate two new nutation series where, in an adjustment, mainly VLBI data (IRIS, GSFC, IERS) have been applied. Contrary to earlier revisions of the present nutation formula, not only the five significantly affected waves (annual, semi-annual, FCN etc.) are corrected but rather all constituents are revised in such a way that white noise residuals result from the adjusted observations, based on the new formula. Still remaining problems (such as the separation of long-period terms from precession etc.) are outlined.

Optical clocks for gravity field observation and further geodetic applications

2020 ◽  
Author(s):  
Hu Wu ◽  
Jürgen Müller ◽  
Annike Knabe
Keyword(s):  
Gravity Field ◽  
Rapid Development ◽  
Satellite Orbit ◽  
Equipotential Surface ◽  
Gravity Potential ◽  
Height Difference ◽  
The Earth ◽  
Temporal Gravity ◽  
Reference Clock

<p>In the past three decades, optical clocks and frequency transfer techniques have experienced a rapid development. They are approaching a fractional frequency uncertainty of 1.0x10<sup>-18</sup>, corresponding to about 1.0 cm in height. This makes them promising to realize “relativistic geodesy”, and it opens a new door to directly obtain gravity potential values by the comparison of clock frequencies. Clocks are thus considered as a novel candidate for determining the Earth’s gravity field. We propose to use a spaceborne clock to obtain gravity potential values along a satellite orbit through its comparison with reference clocks on ground or with a co-orbital clock. The sensitivity of clock measurements is mapped to gravity field coefficients through closed-loop simulations.</p><p>In addition, clocks are investigated for other geodetic applications. Since they are powerful in providing the height difference between distant sites, clocks can be applied for the unification of local/regional height systems, by estimating the offsets between different height datums and the systematic errors within levelling networks. In some regions like Greenland, clocks might be a complementary tool to GRACE(-FO) for detecting temporal gravity signals. They can be operated at locations of interest and continuously track changes w.r.t. reference clock stations. The resulting time-series of gravity potential values reveal the temporal gravity signals at these points. Moreover, as the equipotential surface at a high satellite altitude is more regular than that on the Earth’s surface, a couple of clocks in geostationary orbits can realize a space-based reference for the determination of physical heights at any point on the Earth through clock comparisons.</p><p>We gratefully acknowledge the financial support by the Deutsche Forschungsgemeinschaft (DFG) under Germany’s Excellence Strategy EXC-2123/1 (Project-ID: 390837967).</p>

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